A work in progress, CK-12's Algebra I Second Edition is a clear presentation of algebra for the high school student. Topics include: Equations and Functions, Real Numbers, Equations of Lines, Solving Systems of Equations and Quadratic Equations.

CK-12 Foundation's Basic Algebra FlexBook is an introduction to the algebraic topics of functions, equations, and graphs for middle-school and high-school students.

Students understand that an equation is a statement of equality between two expressions. When values are substituted for the variables in an equation, the equation is either true or false. Students find values to assign to the variables in equations that make the equations true statements.

Students understand that an equation with variables is often viewed as a question asking for the set of values one can assign to the variables of the equation to make the equation a true statement. They see the equation as a “filter” that sifts through all numbers in the domain of the variables, sorting those numbers into two disjoint sets: the Solution Set and the set of numbers for which the equation is false.

Students understand the commutative, associate, and distributive properties as identities, e.g., equations whose solution sets are the set of all values in the domain of the variables.

Students learn if-then moves using the addition and multiplication properties of inequality to solve inequalities and graph the solution sets on the number line.

Students describe the solution set of two equations (or inequalities) joined by either “and” or “or” and graph the solution set on the number line.

Students solve two inequalities joined by “and” or “or,” then graph the solution set on the number line.

Students learn that equations of the form (x - a)(x - b) = 0 have the same solution set as two equations joined by “or:” x - a = 0 or x - b = 0. Students solve factored or easily factorable equations.

Students interpret equations like 1/x = 3 as two equations “1/x = 3 ” and “x ≠ 0 ” joined by “and.” Students find the solution set for this new system of equations.

Students investigate a problem that can be solved by reasoning quantitatively and by creating equations in one variable.
They compare the numerical approach to the algebraic approach.

Using tiles to represent variables and constants, learn how to represent and solve algebra problem. Solve equations, substitute in variable expressions, and expand and factor. Flip tiles, remove zero pairs, copy and arrange, and make your way toward a better understanding of algebra.

This lesson unit is intended to help you assess how well students are able to create and solve linear and non-linear equations. In particular, the lesson will help identify and help students who have the following difficulties: • Solving equations where the unknown appears once or more than once. • Solving equations in more than one way

CK-12 Foundation's Algebra FlexBook is an introduction to algebraic concepts for the high school student. Topics include: Equations & Functions, Real Numbers, Equations of Lines, Solving Systems of Equations & Quadratic Equations.

Students use manipulatives to represent visually the steps they take to obtain a solution to an algebraic equation. They develop an understanding of the connections between the solution involving manipulatives and the symbolic solution.

In this lesson, density will be introduced to students by a demonstration of coke verses diet coke. The teacher will then solve density problems for the students on the board. The class will then complete a lab on the density of plastics. After lab the students will compare results. Each group presents a PowerPoint presentation of their results.

EXERCISING IN SPACE

Algebra 1

Key Topic: Slope, linear equations, direct variation, independent and dependent variables, different representations of a function

Students will identify a direct variation, solve linear equations, and create tables based on the exercise equipment provided for astronauts on long duration missions on the International Space Station (ISS) in order to maintain their fitness to perform mission objectives and to return to Earth without serious health complications.

Students will
identify direct variation from ordered pairs by calculating the constant of variation;
calculate slope from two points using the slope formula;
determine independent and dependent variables;
solve linear equations; and
create tables.

Prerequisites: Students should have prior knowledge of direct variation, the constant of variation, linear functions, different representations of a linear function, the properties of a linear function, calculating slope, and solving linear equations.

The purpose of this task is to apply the equation solving process developed in the previous task to solving literal equations and formulas. Working with literal equations solidifies the notion that operations have to be “un-done” in an appropriate order by doing the inverse operation to both sides of the equation. This task also solidifies the meaning of expressions by attending to the units associated with each of the variables.

The purpose of this task is to solidify student understanding of geometric sequences to
find missing terms in the sequence. Students will draw upon their previous work in using tables
and writing explicit formulas for geometric sequences.

The purpose of this task is to challenge students to reason about inequality relationships and to develop an understanding of the properties of inequalities. Each problem requires reasoning about numbers, including negative numbers and fractions, and thinking mathematically about the various possibilities in the given problem situation.

This lesson will provide students with an introduction to solving equations and inequalities numerically (using a table), graphically, and algebraically.